As finding an analytical solution to minimize eqn:objective is intractable, an iterative majorization algorithm [1]}, [2]}, [3]} is used. We seek to find a manageable surrogate function \(\tau (\mathbf {P}^e, \mathbf {Y})\) , which majorizes \(\sigma (\mathbf {P}^e)\) , i.e., \(\tau (\mathbf {P}^e, \mathbf {Y}) > \sigma (\mathbf {P}^e)\) , with the initial supporting points \(\mathbf {Y}\) .
We can rewrite eqn:objective as follows:
\(\sigma (\mathbf {P}^e) = \sum _{i < j} d_{ij}^2(\mathbf {P}^e) + \sum _{i < j} \delta _{ij}^2 - 2\sum _{i < j}\delta _{ij}d_{ij}(\mathbf {P}^e).\) 
